Holian Brad Lee, Mareschal Michel, Ravelo Ramon
Theoretical Division, <a href="https://ror.org/01e41cf67">Los Alamos National Laboratory</a>, Los Alamos, New Mexico 87545, USA.
Physics Department, <a href="https://ror.org/01r9htc13">Universite Libre de Bruxelles</a>, Bld du triomphe, B1050 Brussels, Belgium.
Phys Rev E. 2024 Jul;110(1-2):015105. doi: 10.1103/PhysRevE.110.015105.
Nonequilibrium molecular dynamics (NEMD) computer simulations of steady shockwaves in dense fluids and rarefied gases produce detailed shockwave profiles of mechanical and thermal properties. The Boltzmann equation, under the assumption of local thermodynamic equilibrium (LTE), leads to the first-order (linear) continuum theory of hydrodynamic flow: Navier-Stokes-Fourier (NSF). (Expansion of the LTE Boltzmann equation in higher powers of gradients yields so-called Burnett second-order terms, etc.) NEMD simulations of strong shockwaves with high gradients are not well modeled by NSF theory. Many years ago, a conjecture for going "beyond Navier-Stokes" was proposed, applying the empirical observation of anisotropic thermal enhancement in the shock front to the temperature dependence of the NSF transport coefficients, whose dissipation determines the slope at the center of the shock profile: for weak shocks, the actual coefficients in NEMD simulations appear to be smaller than in NSF predictions, leading to steeper gradients being observed, while for strong shocks, the NEMD coefficients appear to be larger, leading to less steep shock rises than predicted by NSF calculations. In this paper, we show that adding significant Burnett nonlinearity into an LTE continuum theory reproduces the early shock rise and slope of NEMD profiles, for both weak and strong shocks in dense fluids, as well as strong shockwaves in the ideal gas. Moreover, we show that "Holian's conjecture" incorporates significant Burnett nonlinearity, but like all the other LTE continuum theories, it fails to describe the slow NEMD return to equilibrium beyond the shock front. We show that Maxwell relaxation has to be applied to the hydrodynamic variables themselves (rather than attempting indirect relaxation of their gradients) in order to more accurately model the entire shockwave profile. Non-LTE Maxwell relaxation is the only way to bring the entire profile into agreement with NEMD, most noticeably for strong shockwaves.
对稠密流体和稀薄气体中的稳态激波进行的非平衡分子动力学（NEMD）计算机模拟，产生了机械和热性质的详细激波剖面。在局部热力学平衡（LTE）假设下，玻尔兹曼方程导出了流体动力学流动的一阶（线性）连续介质理论：纳维-斯托克斯-傅里叶（NSF）理论。（LTE玻尔兹曼方程按梯度的更高次幂展开会产生所谓的伯内特二阶项等。）NSF理论无法很好地模拟具有高梯度的强激波的NEMD模拟。许多年前，有人提出了一个“超越纳维-斯托克斯”的猜想，将激波前沿各向异性热增强的经验观察应用于NSF输运系数的温度依赖性，其耗散决定了激波剖面中心的斜率：对于弱激波，NEMD模拟中的实际系数似乎比NSF预测中的小，导致观察到的梯度更陡，而对于强激波，NEMD系数似乎更大，导致激波上升比NSF计算预测的更平缓。在本文中，我们表明，在LTE连续介质理论中加入显著的伯内特非线性，能够再现稠密流体中弱激波和强激波以及理想气体中强激波的NEMD剖面的早期激波上升和斜率。此外，我们表明“霍利安猜想”包含显著的伯内特非线性，但与所有其他LTE连续介质理论一样，它无法描述激波前沿之外NEMD缓慢恢复到平衡的过程。我们表明，必须对流体动力学变量本身应用麦克斯韦弛豫（而不是试图间接弛豫其梯度），以便更准确地模拟整个激波剖面。非LTE麦克斯韦弛豫是使整个剖面与NEMD一致的唯一方法，对于强激波尤为明显。
